Spatial-Kinematic Absorption Models of the Circumgalactic Medium. I. Structures, Orientations, and Kinematics

TL;DR

SKAM provides an analytic, modular framework to synthesize quasar absorption profiles by embedding simple, physically motivated 3D velocity fields within four idealized CGM geometries (spherical halo, bi-polar wind, galactic disk, extended planar accretion). It derives observer and galaxy coordinate transformations, LOS positions, and velocity projection formulas, enabling flexible exploration of arbitrary viewing angles and impact parameters. The work outlines concrete methods for determining LOS intersections with each structure and for combining velocity components into a full LOS velocity $V_{ m LOS}(t)$, laying the groundwork for Paper II to populate the structures with multiphase gas and generate absorption profiles. By enabling rapid, intuitive testing of how geometry and kinematics shape absorption signatures, SKAM offers a valuable interpretive tool bridging simulations and high-resolution quasar spectra, while also revealing degeneracies that require additional spatial or ionization-information to resolve.

Abstract

In this two-paper series, we present a straightforward mathematical model for synthesizing quasar absorption line profiles from sight lines through idealized, spatial-kinematic models of the circumgalactic medium (CGM) and their host galaxies. Here, in Paper I, we develop the spatial geometries of multiple galaxy/CGM structures and populate these structures with 3D velocity fields. For arbitrary viewing angles and galaxy-quasar impact parameters, we derive observer coordinate-based expressions for the perceived azimuthal angle and galaxy inclination and a generalized scalar expression for the line-of-sight velocity as a function of position along the line of sight. We motivate and develop four idealized galaxy/CGM spatial-kinematic structures based on empirical data and theoretical predictions: (1) a rotating galactic disk/extra-planar gas, (2) a static or dynamic spherical halo, (3) an outflowing bi-polar galactic wind, and (4) an inward spiraling flared planar accretion. Using a small set of free parameters, the spatial geometries and velocity fields can be adjusted and explored, including velocity gradients, wind stalling, and accretion trajectories. These spatial-kinematic models are designed to be flexible and easily modified and can be tailored for studying individual galaxy-absorber pairs or galaxy group environments; they can be applied to real-world observations or hydrodynamic simulations of the baryon cycle as studied through quasar absorption line systems. These models also serve as tools for developing physical intuition. In Paper II, we will present the formalism for populating the galaxy/CGM structures with multiphase photoionized and collisionally ionized gas and for generating absorption profiles for ions of interest.

Figures (22)

• Figure 1: Schematic of four idealized CGM spatial-kinematic components; the spherical halo (yellow), the bi-polar outflowing wind (red), the extended planar accretion (blue), and the galactic disk (green) with its ISM and extra-planar gas (EPG). By populating the structures with density, temperature, and velocity fields and running sightlines through the structures, synthetic absorption line systems can be compared to observations.
• Figure 2: The coordinate system $G$$(x,y,z)$ describing the geometry centered on the galaxy (green). Any point at location $P_{\hbox{\tiny G}}(x,y,z)$ can equally be described by its spherical coordinate $P_{\hbox{\tiny G}}(r,\theta,\phi)$. Similarly, any vector can be equally described by its Cartesian unit vectors, ${\hat{\hbox{\bf e}}_x}$, ${\hat{\hbox{\bf e}}_y}$, and ${\hat{\hbox{\bf e}}_z}$, or by its spherical unit vectors ${\hat{\hbox{\bf e}}_r}$, ${\hat{\hbox{\bf e}}_\uptheta}$, and ${\hat{\hbox{\bf e}}_\upphi}$. The axial radius $\rho$, which has unit vector direction ${\hat{\hbox{\bf e}}_\uprho}$, is the projection of ${\bf r}$ on planes of constant $z$. The galaxy and its associated structures are fixed in this coordinate system.
• Figure 3: The observer coordinate system $O$$(x_o,y_o,z_o)$ is rotated about $G$. An observer in $O$ will then see the galaxy with a perspective and orientation dependent on the rotation. System $O$ is rotated twice, first by the angle $\alpha$ around the $z$-axis followed by the angle $\beta$ around the rotated$y_o$ axis. The galaxy is centered at $P_{\hbox{\tiny G}} (0,0,0) = P_{\hbox{\tiny O}}(0,0,0)$.
• Figure 4: The cosmic-eye view of the galaxy coordinate system $G$$(x,y,z)$ and the observer coordinate system $O$$(x_o,y_o,z_o)$, which has been rotated twice, first by the angle $\alpha$ around the $z$-axis of $G$ followed by the angle $\beta$ around the rotated$y_o$ axis. The galaxy is centered at $P_{\hbox{\tiny G}} (0,0,0) = P_{\hbox{\tiny O}}(0,0,0)$. The observer is located at $x_o = +\infty$ and the background quasar is located at $x_o = -\infty$. The LOS (thick black arrow) intersects the sky plane at the coordinates $P_1 = P_{\hbox{\tiny O}}(0,R_\perp \cos \gamma, R_\perp \sin \gamma)$, where $R_\perp$ is the impact parameter and $\gamma$ is the position angle of the quasar on the sky plane. In $G$, this point is denoted $P_1 = P_{\hbox{\tiny G}}(X_0,Y_0,Z_0)$. The LOS is parallel to the $x_o$ axis and has unit vector ${\hat{\hbox{\bf s}}}= - {\hat{\hbox{\bf e}}_{x_o}}$. Note the LOS intersects the $z=0$ plane of the galaxy at point $P_2 = P_{\hbox{\tiny G}}(x_g,y_g,0)$, which is given by Eq \ref{['eq:rhodisk']}.
• Figure 5: A cross-sectional schematic (not to scale) of the idealized spatial structures of the CGM as seen in the galaxy frame, $G$. The "halo" is modeled as a sphere of radius $R_{\hbox{\tiny CGM}}$. The "bi-polar wind" (red) is modeled as a hyperboloid of one sheet described by its opening angle $\Theta_w$, base radius $\rho_{w,0}$, and maximum extent $R_w$. The "disk" (green) is modeled as a finite cylinder with axial radius $\rho_d$ and height $h_d$. The "extended planar accretion" (blue) is also modeled as a hyperboloid of one sheet described by its inner (accretion) radius $\rho_{a,0}$ and maximum extent $R_a$, but the accretion material is confined to void volume outside the solid geometry of the hyperboloid so that the complimentary angle to the opening angle is used; we call it the flare angle, $\Theta_a$.